MATH SOLVE

4 months ago

Q:
# △ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ?

Accepted Solution

A:

Let

b1-------------> base △ABC

b2-------------> base △DEF

A1-----------> area △ABC

A2-----------> area △DEF

we know that

h1=20 in

h2=24 in

A1=b1*20/2-------------> A1=10b1

A2=b2*24/2 ------------> A2=12 b2

if △ABC∼△DEF

then

b1/20=b2/24------------> b1=b2*[20/24]-----> b1=b2*[5/6]

What is the ratio of the area of △ABC to the area of △DEF?

A1=10b1

A2=12b2

A1/A2=(10/12)*(b1/b2)-------> (10/12)*(b2*(5/6)/b2)-----> (10/12)*(5/6)=50/72

A1/A2=50/72--------> 25/36

the answer is (25/36)

b1-------------> base △ABC

b2-------------> base △DEF

A1-----------> area △ABC

A2-----------> area △DEF

we know that

h1=20 in

h2=24 in

A1=b1*20/2-------------> A1=10b1

A2=b2*24/2 ------------> A2=12 b2

if △ABC∼△DEF

then

b1/20=b2/24------------> b1=b2*[20/24]-----> b1=b2*[5/6]

What is the ratio of the area of △ABC to the area of △DEF?

A1=10b1

A2=12b2

A1/A2=(10/12)*(b1/b2)-------> (10/12)*(b2*(5/6)/b2)-----> (10/12)*(5/6)=50/72

A1/A2=50/72--------> 25/36

the answer is (25/36)